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This research establishes the first Wasserstein-2 convergence guarantees for decentralized diffusion models utilizing ODE-based sampling with stochastic velocity fields. By decomposing the velocity field into local experts, the study provides a rigorous theoretical bound of $\mathcal{O}(N^{-1/2}+\varepsilon)$ that accounts for both discretization steps and neural approximation errors. These findings are critical for advancing the mathematical foundations of scalable, privacy-preserving generative AI architectures beyond standard centralized frameworks.
Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition
arXiv:2606.15835v2 Announce Type: replace Abstract: Diffusion models have achieved impressive empirical success in generative tasks, and their convergence theory is now relatively well understood. Motivated by privacy and scalability, recent decentralized diffusion architectures replace a single global velocity field with multiple local experts and a routing mechanism, yielding a sampling dynamics with stochastic expert switching that falls outside standard diffusion convergence analyses. In this work, We study a decentralized diffusion framework with stochastic velocity fields and ODE-based sampling. We establish a convergence guarantee in Wasserstein-2 distance, showing that the distribution of the $N$-step discretization converges to the analytical solution at rate $\mathcal{O}(N^{-1/2}+\varepsilon)$ in $W_2$, where $\varepsilon$ captures the neural approximation errors. To our knowledge, this is the first $W_2$ convergence result for decentralized diffusion models with an ODE-based sampling scheme.
Abstract:Diffusion models have achieved impressive empirical success in generative tasks, and their convergence theory is now relatively well understood. Motivated by privacy and scalability, recent decentralized diffusion architectures replace a single global velocity field with multiple local experts and a routing mechanism, yielding a sampling dynamics with stochastic expert switching that falls outside standard diffusion convergence analyses. In this work, We study a decentralized diffusion framework with stochastic velocity fields and ODE-based sampling. We establish a convergence guarantee in Wasserstein-2 distance, showing that the distribution of the $N$-step discretization converges to the analytical solution at rate $\mathcal{O}(N^{-1/2}+\varepsilon)$ in $W_2$, where $\varepsilon$ captures the neural approximation errors. To our knowledge, this is the first $W_2$ convergence result for decentralized diffusion models with an ODE-based sampling scheme.
50 pages, 9 figures. Preprint under review
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.15835 [cs.LG]
(or arXiv:2606.15835v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.15835 Focus to learn more arXiv-issued DOI via DataCite
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